Uncertainty principles of Ingham and Paley–Wiener on semisimple Lie groups

Authors

Mithun Bhowmik, Indian Statistical Institute, Kolkata
Suparna Sen, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Israel Journal of Mathematics

Abstract

Classical results due to Ingham and Paley–Wiener characterize the existence of nonzero functions supported on certain subsets of the real line in terms of the pointwise decay of the Fourier transforms. Viewing these results as uncertainty principles for Fourier transforms, we prove certain analogues of these results on connected, noncompact, semisimple Lie groups with finite center. We also use these results to show a unique continuation property of solutions to the initial value problem for time-dependent Schrödinger equations on Riemmanian symmetric spaces of noncompact type.

First Page

193

Last Page

221

DOI

10.1007/s11856-018-1662-8

Publication Date

4-1-2018

Comments

All Open Access, Green

Recommended Citation

Bhowmik, Mithun and Sen, Suparna, "Uncertainty principles of Ingham and Paley–Wiener on semisimple Lie groups" (2018). Journal Articles. 1418.
https://digitalcommons.isical.ac.in/journal-articles/1418